This can result from multiple device drivers cluttering the input to the game. Check in your device manager under human interface devices for a driver(s) called HID-compliant game controller. If there are multiple, odds are these are the root of the problem. Delete any that you are not using and load the game again.
Alternately, if you have a problem where pressing the stick right will cause the car to turn right for a bit and then stop, and pushing left causes the same issue, you are probably in ‘Directional Control’ mode (which is the default) - in this mode, you steer by pushing the stick in the direction you want the car to go (ie: pushing right on the stick will make the car turn to face the right-hand side of the screen.
Pushing left on the stick will make the car turn to face the left side of the screen. If you want the car to go ‘up’ the screen, push up on the stick).
While this may seem unintuitive at first, its the best way to play the game! However, if you would prefer a left/right steering control method, you can change the controls in the options menu.